Mathematical and Statistical Foundations for AI
Part of the Applied AI Security and Assurance curriculum, authored by Cameron Hopkin, CISSP, CEH, CHFI. Published as a reference, not an enrollable course.
Description
The honest mathematical foundation, modernized and pointed at what breaks in real systems. Linear algebra, matrix decompositions, optimization, probability, and statistics, each framed toward downstream security and evaluation concerns rather than taught in isolation.
Outcomes
- Implement core numerical methods from scratch.
- Reason about conditioning, convergence, and where optimization fails.
- Quantify and communicate uncertainty and calibration.
Modules
- Linear algebra and the geometry of high-dimensional space.
- Matrix decompositions and why they matter.
- Optimization: gradient methods, convexity, and failure modes.
- Probability and statistics for machine learning.
- Calibration and uncertainty.
- Reproducibility and numerical stability.
Signature lab
Implement backpropagation and an optimizer from scratch in PyTorch, then break it with a poorly conditioned problem and diagnose why. PyTorch is the deliberate choice: it is the framework of the research literature this curriculum trains people to read and extend, used in roughly 85 percent of published deep learning research [4].
Research thread
Reproducibility and numerical stability as preconditions for any trustworthy result.